I would say, as a non-Christian agnostic (Who has given some thought to Christian conversion, as well as to alternate brands of Theism, IE: Sikhism, Sufism, etc), that the "God-shaped hole", as it were, originates not so much from the fact that God "designed" us to seek Him out, but from the fact that humans evolved a self-awareness that transcends that of the "Lower" forms of animal life. With that self-awareness came the sense of individuation, the sense that I am, in some sense, while being part of the world, distinct from it as well: I am me, and the experience of being myself is one that I cannot replicate, or describe in it's totality to another individual.
That sense of individualism and distinction and the recognition that one possesses a life that is bound to end at some point or another invariably leads one to ask, at one point or another, the "Big questions": Where am I going, what am I here for, what happens when I die, and so forth, which gives rise to a sense of existential despair or angst, as Sartre would put it, which is notoriously difficult to assuage, which one could liken to a "God-Shaped Hole". I don't necessarily agree with the idea that everybody has such a hole in their lives which only God can fill, however. Some people find fulfillment in what they consider to be a relationship with God, which it may well be, but which I cannot judge as such on the outside looking in.
Other people, however "leave the fold" precisely because the passion they once had for their belief is lost, and the hole that God was supposed to fill is intruding upon their consciousness. Other people fill that void through intellectual pursuits, or by finding a relationship with like minded people, volunteering their time to their community, or by pursuing other hobbies. No two people are exact "Carbon Copies" of one another, and therefore what works to enliven one person's life and offer them some sort of wholeness, may not work for another person.
At any rate, I've continued on for long enough. If anybody would like to engage me on any the points I've written above, greet me to your humble abode, etc, please feel free and I will see about getting back to you
Update: I removed a paragraph from my initial post. In retrospect, it appeared condescending and does not reflect the spirit of the Golden Rule, to treat others as you would be wish to be treated. There are personal reflections which are best left not shared in particular venues, when such viewpoints may hurt another person unawares. As to the suggestion to add sources so as to make my response more "scholarly" (though I myself am not a scholar by any means), I have taken that suggestion to heart.
On the issue of self-awareness of oneself producing a fear of dread and existential despair, I would direct one first and foremost to the philosophy of Martin Heidegger. A good resource that is not mired in philosophical jargon and accessible to the layman/woman can be found at the following link:
In particular, the following paragraph (Especially the last two sentences) is extremely instructive in getting across what I was trying to convey in my original message:
"What is first glimpsed in anxiety is the authentic self. As the world slips away, we obtrude. I like to think about this in maritime terms. Inauthentic life in the world is completely bound up with things and other people in a kind of "groundless floating" – the phrase is Heidegger's. Everyday life in the world is like being immersed in the sea and drowned by the world's suffocating banality. Anxiety is the experience of the tide going out, the seawater draining away, revealing a self stranded on the strand, as it were. Anxiety is that basic mood when the self first distinguishes itself from the world and becomes self-aware."
What the above article tries to get at is that there is a certain sense in which our awareness reveals to us a sense of the banality and triviality of everyday life and our subsequent desire, in the face of said world, to make our lives more "real" than the world around us, to find meaning in something that transcends ourselves. At the theater, such themes can be seen in movies such as the Matrix and the Truman Show, or for a slightly older example, Groundhog Day (which borrowed the idea of the Eternal Return and the "Sacred Yes" from the thought of Nietzsche).